Depending on the exact nature of the duty: “guarding”, “watching”, “minding”, “running”, but they each suggest something more specific and active than is required by “manning”, which means to turn up and be there.

“Occupying” is close to a synonym, but slightly suggests that it’s not merely present, you’re preventing another person from occupying the same desk.

What’s you doing with “tending”?

“Staffing” can mean “to do the duty”, or “to ensure someone’s on it, not necessarily yourself”, or “to provide staff”. What it has an appropriate meaning but is potentially more general. As far as I know it’s nevertheless the “standard” alternative in this context.